How many pairs of integers (a, b) are necessary to make sure that for two of them, say and it is the case that and ?

Dirichlet (or Pigeonhole) Principle talks about pigeons and holes. I suggest considering pairs where as pigeons and pairs where and as holes. A pigeon is in the hole if and . You have to check that having two pigeons in one hole corresponds to the condition in the problem statement, as well as to find out the number of holes.